本文整理汇总了Python中sympy.polys.densearith.dmp_quo函数的典型用法代码示例。如果您正苦于以下问题：Python dmp_quo函数的具体用法？Python dmp_quo怎么用？Python dmp_quo使用的例子？那么恭喜您, 这里精选的函数代码示例或许可以为您提供帮助。
在下文中一共展示了dmp_quo函数的15个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: _dmp_simplify_gcd
def _dmp_simplify_gcd(f, g, u, K):
"""Try to eliminate `x_0` from GCD computation in `K[X]`. """
df = dmp_degree(f, u)
dg = dmp_degree(g, u)
if df > 0 and dg > 0:
return None
if not (df or dg):
F = dmp_LC(f, K)
G = dmp_LC(g, K)
else:
if not df:
F = dmp_LC(f, K)
G = dmp_content(g, u, K)
else:
F = dmp_content(f, u, K)
G = dmp_LC(g, K)
v = u - 1
h = dmp_gcd(F, G, v, K)
cff = [ dmp_quo(cf, h, v, K) for cf in f ]
cfg = [ dmp_quo(cg, h, v, K) for cg in g ]
return [h], cff, cfg示例2: dmp_discriminant
def dmp_discriminant(f, u, K):
"""
Computes discriminant of a polynomial in `K[X]`.
Examples
========
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.euclidtools import dmp_discriminant
>>> f = ZZ.map([[[[1]], [[]]], [[[1], []]], [[[1, 0]]]])
>>> dmp_discriminant(f, 3, ZZ)
[[[-4, 0]], [[1], [], []]]
"""
if not u:
return dup_discriminant(f, K)
d, v = dmp_degree(f, u), u-1
if d <= 0:
return dmp_zero(v)
else:
s = (-1)**((d*(d-1)) // 2)
c = dmp_LC(f, K)
r = dmp_resultant(f, dmp_diff(f, 1, u, K), u, K)
c = dmp_mul_ground(c, K(s), v, K)
return dmp_quo(r, c, v, K)示例3: dmp_sqf_part
def dmp_sqf_part(f, u, K):
"""
Returns square-free part of a polynomial in ``K[X]``.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y = ring("x,y", ZZ)
>>> R.dmp_sqf_part(x**3 + 2*x**2*y + x*y**2)
x**2 + x*y
"""
if not u:
return dup_sqf_part(f, K)
if K.is_FiniteField:
return dmp_gf_sqf_part(f, u, K)
if dmp_zero_p(f, u):
return f
if K.is_negative(dmp_ground_LC(f, u, K)):
f = dmp_neg(f, u, K)
gcd = dmp_gcd(f, dmp_diff(f, 1, u, K), u, K)
sqf = dmp_quo(f, gcd, u, K)
if K.has_Field:
return dmp_ground_monic(sqf, u, K)
else:
return dmp_ground_primitive(sqf, u, K)[1]示例4: dmp_discriminant
def dmp_discriminant(f, u, K):
"""
Computes discriminant of a polynomial in `K[X]`.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y,z,t = ring("x,y,z,t", ZZ)
>>> R.dmp_discriminant(x**2*y + x*z + t)
-4*y*t + z**2
"""
if not u:
return dup_discriminant(f, K)
d, v = dmp_degree(f, u), u - 1
if d <= 0:
return dmp_zero(v)
else:
s = (-1)**((d*(d - 1)) // 2)
c = dmp_LC(f, K)
r = dmp_resultant(f, dmp_diff(f, 1, u, K), u, K)
c = dmp_mul_ground(c, K(s), v, K)
return dmp_quo(r, c, v, K)示例5: dmp_rr_lcm
def dmp_rr_lcm(f, g, u, K):
"""
Computes polynomial LCM over a ring in `K[X]`.
Examples
========
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.euclidtools import dmp_rr_lcm
>>> f = ZZ.map([[1], [2, 0], [1, 0, 0]])
>>> g = ZZ.map([[1], [1, 0], []])
>>> dmp_rr_lcm(f, g, 1, ZZ)
[[1], [2, 0], [1, 0, 0], []]
"""
fc, f = dmp_ground_primitive(f, u, K)
gc, g = dmp_ground_primitive(g, u, K)
c = K.lcm(fc, gc)
h = dmp_quo(dmp_mul(f, g, u, K),
dmp_gcd(f, g, u, K), u, K)
return dmp_mul_ground(h, c, u, K)示例6: test_dmp_div
def test_dmp_div():
f, g, q, r = [5,4,3,2,1], [1,2,3], [5,-6,0], [20,1]
assert dmp_div(f, g, 0, ZZ) == (q, r)
assert dmp_quo(f, g, 0, ZZ) == q
assert dmp_rem(f, g, 0, ZZ) == r
raises(ExactQuotientFailed, lambda: dmp_exquo(f, g, 0, ZZ))
f, g, q, r = [[[1]]], [[[2]],[1]], [[[]]], [[[1]]]
assert dmp_div(f, g, 2, ZZ) == (q, r)
assert dmp_quo(f, g, 2, ZZ) == q
assert dmp_rem(f, g, 2, ZZ) == r
raises(ExactQuotientFailed, lambda: dmp_exquo(f, g, 2, ZZ))示例7: dmp_sqf_part
def dmp_sqf_part(f, u, K):
"""
Returns square-free part of a polynomial in ``K[X]``.
Examples
========
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.sqfreetools import dmp_sqf_part
>>> f = ZZ.map([[1], [2, 0], [1, 0, 0], []])
>>> dmp_sqf_part(f, 1, ZZ)
[[1], [1, 0], []]
"""
if not u:
return dup_sqf_part(f, K)
if not K.has_CharacteristicZero:
return dmp_gf_sqf_part(f, u, K)
if dmp_zero_p(f, u):
return f
if K.is_negative(dmp_ground_LC(f, u, K)):
f = dmp_neg(f, u, K)
gcd = dmp_gcd(f, dmp_diff(f, 1, u, K), u, K)
sqf = dmp_quo(f, gcd, u, K)
if K.has_Field or not K.is_Exact:
return dmp_ground_monic(sqf, u, K)
else:
return dmp_ground_primitive(sqf, u, K)[1]示例8: dmp_rr_lcm
def dmp_rr_lcm(f, g, u, K):
"""
Computes polynomial LCM over a ring in `K[X]`.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y, = ring("x,y", ZZ)
>>> f = x**2 + 2*x*y + y**2
>>> g = x**2 + x*y
>>> R.dmp_rr_lcm(f, g)
x**3 + 2*x**2*y + x*y**2
"""
fc, f = dmp_ground_primitive(f, u, K)
gc, g = dmp_ground_primitive(g, u, K)
c = K.lcm(fc, gc)
h = dmp_quo(dmp_mul(f, g, u, K),
dmp_gcd(f, g, u, K), u, K)
return dmp_mul_ground(h, c, u, K)示例9: dmp_rr_prs_gcd
def dmp_rr_prs_gcd(f, g, u, K):
"""
Computes polynomial GCD using subresultants over a ring.
Returns ``(h, cff, cfg)`` such that ``a = gcd(f, g)``, ``cff = quo(f, h)``,
and ``cfg = quo(g, h)``.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y, = ring("x,y", ZZ)
>>> f = x**2 + 2*x*y + y**2
>>> g = x**2 + x*y
>>> R.dmp_rr_prs_gcd(f, g)
(x + y, x + y, x)
"""
if not u:
return dup_rr_prs_gcd(f, g, K)
result = _dmp_rr_trivial_gcd(f, g, u, K)
if result is not None:
return result
fc, F = dmp_primitive(f, u, K)
gc, G = dmp_primitive(g, u, K)
h = dmp_subresultants(F, G, u, K)[-1]
c, _, _ = dmp_rr_prs_gcd(fc, gc, u - 1, K)
if K.is_negative(dmp_ground_LC(h, u, K)):
h = dmp_neg(h, u, K)
_, h = dmp_primitive(h, u, K)
h = dmp_mul_term(h, c, 0, u, K)
cff = dmp_quo(f, h, u, K)
cfg = dmp_quo(g, h, u, K)
return h, cff, cfg示例10: dmp_rr_prs_gcd
def dmp_rr_prs_gcd(f, g, u, K):
"""
Computes polynomial GCD using subresultants over a ring.
Returns ``(h, cff, cfg)`` such that ``a = gcd(f, g)``, ``cff = quo(f, h)``,
and ``cfg = quo(g, h)``.
Examples
========
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.euclidtools import dmp_rr_prs_gcd
>>> f = ZZ.map([[1], [2, 0], [1, 0, 0]])
>>> g = ZZ.map([[1], [1, 0], []])
>>> dmp_rr_prs_gcd(f, g, 1, ZZ)
([[1], [1, 0]], [[1], [1, 0]], [[1], []])
"""
if not u:
return dup_rr_prs_gcd(f, g, K)
result = _dmp_rr_trivial_gcd(f, g, u, K)
if result is not None:
return result
fc, F = dmp_primitive(f, u, K)
gc, G = dmp_primitive(g, u, K)
h = dmp_subresultants(F, G, u, K)[-1]
c, _, _ = dmp_rr_prs_gcd(fc, gc, u-1, K)
if K.is_negative(dmp_ground_LC(h, u, K)):
h = dmp_neg(h, u, K)
_, h = dmp_primitive(h, u, K)
h = dmp_mul_term(h, c, 0, u, K)
cff = dmp_quo(f, h, u, K)
cfg = dmp_quo(g, h, u, K)
return h, cff, cfg示例11: dmp_ff_prs_gcd
def dmp_ff_prs_gcd(f, g, u, K):
"""
Computes polynomial GCD using subresultants over a field.
Returns ``(h, cff, cfg)`` such that ``a = gcd(f, g)``, ``cff = quo(f, h)``,
and ``cfg = quo(g, h)``.
Examples
========
>>> from sympy.polys.domains import QQ
>>> from sympy.polys.euclidtools import dmp_ff_prs_gcd
>>> f = [[QQ(1,2)], [QQ(1), QQ(0)], [QQ(1,2), QQ(0), QQ(0)]]
>>> g = [[QQ(1)], [QQ(1), QQ(0)], []]
>>> dmp_ff_prs_gcd(f, g, 1, QQ)
([[1/1], [1/1, 0/1]], [[1/2], [1/2, 0/1]], [[1/1], []])
"""
if not u:
return dup_ff_prs_gcd(f, g, K)
result = _dmp_ff_trivial_gcd(f, g, u, K)
if result is not None:
return result
fc, F = dmp_primitive(f, u, K)
gc, G = dmp_primitive(g, u, K)
h = dmp_subresultants(F, G, u, K)[-1]
c, _, _ = dmp_ff_prs_gcd(fc, gc, u-1, K)
_, h = dmp_primitive(h, u, K)
h = dmp_mul_term(h, c, 0, u, K)
h = dmp_ground_monic(h, u, K)
cff = dmp_quo(f, h, u, K)
cfg = dmp_quo(g, h, u, K)
return h, cff, cfg示例12: dmp_ff_prs_gcd
def dmp_ff_prs_gcd(f, g, u, K):
"""
Computes polynomial GCD using subresultants over a field.
Returns ``(h, cff, cfg)`` such that ``a = gcd(f, g)``, ``cff = quo(f, h)``,
and ``cfg = quo(g, h)``.
Examples
========
>>> from sympy.polys import ring, QQ
>>> R, x,y, = ring("x,y", QQ)
>>> f = QQ(1,2)*x**2 + x*y + QQ(1,2)*y**2
>>> g = x**2 + x*y
>>> R.dmp_ff_prs_gcd(f, g)
(x + y, 1/2*x + 1/2*y, x)
"""
if not u:
return dup_ff_prs_gcd(f, g, K)
result = _dmp_ff_trivial_gcd(f, g, u, K)
if result is not None:
return result
fc, F = dmp_primitive(f, u, K)
gc, G = dmp_primitive(g, u, K)
h = dmp_subresultants(F, G, u, K)[-1]
c, _, _ = dmp_ff_prs_gcd(fc, gc, u - 1, K)
_, h = dmp_primitive(h, u, K)
h = dmp_mul_term(h, c, 0, u, K)
h = dmp_ground_monic(h, u, K)
cff = dmp_quo(f, h, u, K)
cfg = dmp_quo(g, h, u, K)
return h, cff, cfg示例13: dmp_ff_lcm
def dmp_ff_lcm(f, g, u, K):
"""
Computes polynomial LCM over a field in ``K[X]``.
**Examples**
>>> from sympy.polys.domains import QQ
>>> from sympy.polys.euclidtools import dmp_ff_lcm
>>> f = [[QQ(1,4)], [QQ(1), QQ(0)], [QQ(1), QQ(0), QQ(0)]]
>>> g = [[QQ(1,2)], [QQ(1), QQ(0)], []]
>>> dmp_ff_lcm(f, g, 1, QQ)
[[1/1], [4/1, 0/1], [4/1, 0/1, 0/1], []]
"""
h = dmp_quo(dmp_mul(f, g, u, K),
dmp_gcd(f, g, u, K), u, K)
return dmp_ground_monic(h, u, K)示例14: dmp_ff_lcm
def dmp_ff_lcm(f, g, u, K):
"""
Computes polynomial LCM over a field in `K[X]`.
Examples
========
>>> from sympy.polys import ring, QQ
>>> R, x,y, = ring("x,y", QQ)
>>> f = QQ(1,4)*x**2 + x*y + y**2
>>> g = QQ(1,2)*x**2 + x*y
>>> R.dmp_ff_lcm(f, g)
x**3 + 4*x**2*y + 4*x*y**2
"""
h = dmp_quo(dmp_mul(f, g, u, K), dmp_gcd(f, g, u, K), u, K)
return dmp_ground_monic(h, u, K)示例15: dmp_primitive
def dmp_primitive(f, u, K):
"""
Returns multivariate content and a primitive polynomial.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y, = ring("x,y", ZZ)
>>> R.dmp_primitive(2*x*y + 6*x + 4*y + 12)
(2*y + 6, x + 2)
"""
cont, v = dmp_content(f, u, K), u - 1
if dmp_zero_p(f, u) or dmp_one_p(cont, v, K):
return cont, f
else:
return cont, [ dmp_quo(c, cont, v, K) for c in f ]